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Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Contact

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

Nutrition and Cycling

Age 14 to 16 Challenge Level:

How could you organise the cards?
Are there any pieces of information you haven't used yet?
Are there any cards with useless information?
Could you combine the information on several cards to generate new pieces of information?